Mirror Descent Policy Optimisation for Robust Constrained Markov Decision Processes
This work addresses safety and robustness in reinforcement learning systems, particularly for applications requiring constraint satisfaction under uncertainty, though it appears incremental as it builds on existing policy gradient and robust MDP frameworks.
The paper tackles the problem of learning safe reinforcement learning policies under uncertainty by proposing mirror descent policy optimization for robust constrained Markov decision processes, achieving an O~(1/T^{1/3}) convergence rate and showing significant robustness improvements in experiments.
Safety is an essential requirement for reinforcement learning systems. The newly emerging framework of robust constrained Markov decision processes allows learning policies that satisfy long-term constraints while providing guarantees under epistemic uncertainty. This paper presents mirror descent policy optimisation for robust constrained Markov decision processes, making use of policy gradient techniques to optimise both the policy (as a maximiser) and the transition kernel (as an adversarial minimiser) on the Lagrangian representing a constrained Markov decision process. Our proposed algorithm obtains an $\tilde{\mathcal{O}}\left(1/T^{1/3}\right)$ convergence rate in the sample-based robust constrained Markov decision process setting. The paper also contributes an algorithm for approximate gradient descent in the space of transition kernels, which is of independent interest for designing adversarial environments in general Markov decision processes. Experiments confirm the benefits of mirror descent policy optimisation in constrained and unconstrained optimisation, and significant improvements are observed in robustness tests when compared to baseline policy optimisation algorithms.